From Wikipedia, the free encyclopedia
(Redirected from Classifying space for O)

In mathematics, the classifying space for the orthogonal group O(n) may be constructed as the Grassmannian of n-planes in an infinite-dimensional real space .

Cohomology ring

The cohomology ring of with coefficients in the field of two elements is generated by the Stiefel–Whitney classes: [1] [2]

Infinite classifying space

The canonical inclusions induce canonical inclusions on their respective classifying spaces. Their respective colimits are denoted as:

is indeed the classifying space of .

See also

Literature

  • Milnor, John; Stasheff, James (1974). Characteristic classes (PDF). Princeton University Press. doi: 10.1515/9781400881826. ISBN  9780691081229.
  • Hatcher, Allen (2002). Algebraic topology. Cambridge: Cambridge University Press. ISBN  0-521-79160-X.
  • Mitchell, Stephen (August 2001). Universal principal bundles and classifying spaces (PDF).

External links

References

  1. ^ Milnor & Stasheff, Theorem 7.1 on page 83
  2. ^ Hatcher 02, Theorem 4D.4.
From Wikipedia, the free encyclopedia
(Redirected from Classifying space for O)

In mathematics, the classifying space for the orthogonal group O(n) may be constructed as the Grassmannian of n-planes in an infinite-dimensional real space .

Cohomology ring

The cohomology ring of with coefficients in the field of two elements is generated by the Stiefel–Whitney classes: [1] [2]

Infinite classifying space

The canonical inclusions induce canonical inclusions on their respective classifying spaces. Their respective colimits are denoted as:

is indeed the classifying space of .

See also

Literature

  • Milnor, John; Stasheff, James (1974). Characteristic classes (PDF). Princeton University Press. doi: 10.1515/9781400881826. ISBN  9780691081229.
  • Hatcher, Allen (2002). Algebraic topology. Cambridge: Cambridge University Press. ISBN  0-521-79160-X.
  • Mitchell, Stephen (August 2001). Universal principal bundles and classifying spaces (PDF).

External links

References

  1. ^ Milnor & Stasheff, Theorem 7.1 on page 83
  2. ^ Hatcher 02, Theorem 4D.4.

Videos

Youtube | Vimeo | Bing

Websites

Google | Yahoo | Bing

Encyclopedia

Google | Yahoo | Bing

Facebook